Processing math: 0%

The Stacks project

Lemma 88.30.3. Let A \to B be a local map of local Noetherian rings such that

  1. A \to B is flat,

  2. \mathfrak m_ B = \mathfrak m_ A B, and

  3. \kappa (\mathfrak m_ A) = \kappa (\mathfrak m_ B)

Then the base change functor from the category (88.30.0.1) for (A, \mathfrak m_ A) to the category (88.30.0.1) for (B, \mathfrak m_ B) is an equivalence.

Proof. The conditions signify that A \to B induces an isomorphism on completions, see More on Algebra, Lemma 15.43.9. Hence this lemma is a special case of Lemma 88.30.1. \square

Comments (0)

There are also:

  • 1 comment(s) on Section 88.30: Application to modifications

Post a comment

Your email address will not be published. Required fields are marked.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.




In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 0AF7. Beware of the difference between the letter 'O' and the digit '0'.



View Lemma 88.30.3 as pdf